Re: Simplifying with assumptions

• To: mathgroup at smc.vnet.net
• Subject: [mg48992] Re: [mg48949] Simplifying with assumptions
• From: DrBob <drbob at bigfoot.com>
• Date: Sat, 26 Jun 2004 01:55:36 -0400 (EDT)
• References: <200406250658.CAA12398@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Here's a step that may be SLIGHTLY useful:

Reduce[y == Sqrt[48 - n^2 + 8*x] && n \[Element]
Integers && x \[Element]
Integers && y \[Element]
Integers]

(n | x | y) \[Element] Integers &&
y >= 0 && x >=
(1/8)*(-48 + y^2) &&
(n == -Sqrt[48 + 8*x -
y^2] || n ==
Sqrt[48 + 8*x - y^2])

or

Solve[y == Sqrt[48 - n^2 +
8*x], x]
Solve[y == Sqrt[48 - n^2 +
8*x], n]
{{x -> (1/8)*(-48 + n^2 +
y^2)}}
{{n -> -Sqrt[48 + 8*x -
y^2]},
{n -> Sqrt[48 + 8*x - y^2]}}

Bobby

On Fri, 25 Jun 2004 02:58:13 -0400 (EDT), Mietek Bak <mietek at icpnet.pl> wrote:

> Hello,
>
> I'm a complete newcomer to Mathematica, so please excuse this possibly
> silly question.
>
> I'm trying to determine if a formula will ever give an integer result,
> assuming that all variables used in it are integer.  I've been searching
> through the built-in documentation, but my best guess didn't really do
> anything:
>
> Simplify[Element[Sqrt[48 - n^2 + 8*x],Integers],Element[{n, x},Integers]]
>
> It would be best if I could somehow determine the set of combinations of
> variables that would give an integer result -- if there are any.  Is
> there a way to do that in Mathematica?
>
> Mietek Bak.
>
>

--
DrBob at bigfoot.com
www.eclecticdreams.net

```

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